Circle Theorem

Front

What is a circle theorem?

Back

Circle theorems are rules that describe the relationships between angles, arcs, and chords in a circle.

Tags

CCSS.HSG.CO.C.9

Front

What is the angle in a semicircle?

Back

The angle subtended by a semicircle is a right angle (90 degrees).

Tags

CCSS.HSG.C.A.2

Front

What is the tangent-secant theorem?

Back

If a tangent and a secant are drawn from a point outside a circle, the square of the length of the tangent is equal to the product of the lengths of the secant segment and its external segment.

Tags

CCSS.HSG.C.A.2

Front

What is the alternate segment theorem?

Back

The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.

Tags

CCSS.HSG.C.A.2

Front

If two chords intersect inside a circle, what is the relationship between the angles formed?

Back

The angles formed are equal to half the sum of the measures of the arcs intercepted by the angles.

Tags

CCSS.HSG.C.A.2

Front

What is the inscribed angle theorem?

Back

The measure of an inscribed angle is half the measure of the intercepted arc.

Tags

CCSS.HSG.C.A.2

Front

What is the relationship between angles subtended by the same arc?

Back

Angles subtended by the same arc at the circumference of the circle are equal.

Tags

CCSS.HSG.C.A.2

Front

What is the relationship between the angles in the same segment of a circle?

Back

Angles in the same segment of a circle are equal.

Tags

CCSS.HSG.C.A.2

Front

What is the angle subtended by a diameter at the circumference?

Back

The angle subtended by a diameter at the circumference is a right angle (90 degrees).

Tags

CCSS.HSG.C.A.2

Front

If two tangents are drawn from a point outside a circle, what is the relationship between the angles formed?

Back

The angles formed between the tangents and the line connecting the point to the center of the circle are equal.

Tags

CCSS.HSG.C.A.2